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   <div id="projectname">DiscontinuousGalerkin
   &#160;<span id="projectnumber">0.0.1</span>
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   <div id="projectbrief">Geração Acoplada de Discontinuous Galerkin</div>
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<div class="title">SquareElement.f90</div>  </div>
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<a href="_square_element_8f90.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a><a class="code" href="class_square_element_manipulation.html">00001</a> <span class="keyword">module</span> <a class="code" href="class_square_element_manipulation.html">SquareElementManipulation</a>
<a name="l00002"></a>00002     use <span class="keywordflow">MatrixOperation</span>
<a name="l00003"></a>00003     use <span class="keywordflow">GaussianIntegration</span>
<a name="l00004"></a>00004     <span class="keyword">implicit none</span>
<a name="l00005"></a>00005 
<a name="l00006"></a><a class="code" href="struct_square_element_manipulation_1_1_square_element.html">00006</a>     <span class="keyword">type</span> <a class="code" href="struct_square_element_manipulation_1_1_square_element.html">SquareElement</a>
<a name="l00007"></a><a class="code" href="struct_square_element_manipulation_1_1_square_element.html#ab23b0464230de3342a71acbb4d49e808">00007</a>         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(12,13)</span> :: Matrix
<a name="l00008"></a><a class="code" href="struct_square_element_manipulation_1_1_square_element.html#abd1c024b52c93f0409a76057f8831230">00008</a>         <span class="keywordtype">integer</span>, <span class="keywordtype">dimension(4)</span>          :: Nodes
<a name="l00009"></a><a class="code" href="struct_square_element_manipulation_1_1_square_element.html#a5ff1c81d9b7defe1122114f39582edeb">00009</a>         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(12)</span>    :: DoF
<a name="l00010"></a>00010 <span class="keyword">    end type</span>
<a name="l00011"></a>00011 
<a name="l00012"></a>00012 <span class="keyword">contains</span>
<a name="l00013"></a>00013 
<a name="l00014"></a><a class="code" href="class_square_element_manipulation.html#ac5893e16b45b75e3d5b7528318d495ff">00014</a>     <span class="keyword">subroutine </span>SetNodesSquareElement( this, Nodes)
<a name="l00015"></a>00015         <span class="keyword">implicit none</span>
<a name="l00016"></a>00016         <span class="keywordtype">type(SquareElement)</span>, <span class="keywordtype">intent(out)</span> :: this
<a name="l00017"></a>00017         <span class="keywordtype">integer</span>, <span class="keywordtype">dimension(4)</span>, <span class="keywordtype">intent(in)</span> :: Nodes
<a name="l00018"></a>00018 
<a name="l00019"></a>00019         this%Nodes(1) = Nodes(1)
<a name="l00020"></a>00020         this%Nodes(2) = Nodes(2)
<a name="l00021"></a>00021         this%Nodes(3) = Nodes(3)
<a name="l00022"></a>00022         this%Nodes(4) = Nodes(4)
<a name="l00023"></a>00023 
<a name="l00024"></a>00024         this%Matrix = 0.0d0
<a name="l00025"></a>00025         this%DoF = 0.0d0
<a name="l00026"></a>00026 <span class="keyword">    end subroutine</span>
<a name="l00027"></a>00027 
<a name="l00028"></a><a class="code" href="class_square_element_manipulation.html#a7f29d1f9546b3b53a42d4f9aae7ae272">00028</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>phi(i, eta1, eta2) result (v)
<a name="l00029"></a>00029         <span class="keyword">implicit none</span>
<a name="l00030"></a>00030         <span class="keywordtype">integer(kind=1)</span>, <span class="keywordtype">intent(in)</span> :: i
<a name="l00031"></a>00031         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: eta1
<a name="l00032"></a>00032         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: eta2
<a name="l00033"></a>00033 
<a name="l00034"></a>00034         <span class="keywordtype">real(kind=8)</span> :: v
<a name="l00035"></a>00035 
<a name="l00036"></a>00036         <span class="keyword">select</span> <span class="keyword">case</span>(i)
<a name="l00037"></a>00037             <span class="keyword">case</span>(1)
<a name="l00038"></a>00038                 v = (1.0d0-eta1)*(1.0d0-eta2)/4.0d0
<a name="l00039"></a>00039             <span class="keyword">case</span>(2)
<a name="l00040"></a>00040                 v = (1.0d0+eta1)*(1.0d0-eta2)/4.0d0
<a name="l00041"></a>00041             <span class="keyword">case</span>(3)
<a name="l00042"></a>00042                 v = (1.0d0+eta1)*(1.0d0+eta2)/4.0d0
<a name="l00043"></a>00043             <span class="keyword">case</span>(4)
<a name="l00044"></a>00044                 v = (1.0d0-eta1)*(1.0d0+eta2)/4.0d0
<a name="l00045"></a>00045             <span class="keyword">case</span> default
<a name="l00046"></a>00046                 v = 0.0d0
<a name="l00047"></a>00047         <span class="keyword">end select</span>
<a name="l00048"></a>00048 <span class="keyword">    end function</span>
<a name="l00049"></a>00049 
<a name="l00050"></a><a class="code" href="class_square_element_manipulation.html#aa7eb9802507b55df7d8bcc751112aeb2">00050</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>dphi(i, j, eta1, eta2) result (v)
<a name="l00051"></a>00051         <span class="keyword">implicit none</span>
<a name="l00052"></a>00052         <span class="keywordtype">integer(kind=1)</span>, <span class="keywordtype">intent(in)</span> :: i
<a name="l00053"></a>00053         <span class="keywordtype">integer(kind=1)</span>, <span class="keywordtype">intent(in)</span> :: j
<a name="l00054"></a>00054         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: eta1
<a name="l00055"></a>00055         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: eta2
<a name="l00056"></a>00056 
<a name="l00057"></a>00057         <span class="keywordtype">real(kind=8)</span> :: v
<a name="l00058"></a>00058 
<a name="l00059"></a>00059         <span class="keyword">select</span> <span class="keyword">case</span>(i)
<a name="l00060"></a>00060             <span class="keyword">case</span>(1)
<a name="l00061"></a>00061                 <span class="keyword">select</span> <span class="keyword">case</span>(j)
<a name="l00062"></a>00062                     <span class="keyword">case</span>(1)
<a name="l00063"></a>00063                         v = (eta2-1.0d0)/4.0d0
<a name="l00064"></a>00064                     <span class="keyword">case</span>(2)
<a name="l00065"></a>00065                         v = (eta1-1.0d0)/4.0d0
<a name="l00066"></a>00066                     <span class="keyword">case</span> default
<a name="l00067"></a>00067                         v = 0.0d0
<a name="l00068"></a>00068                 <span class="keyword">end select</span>
<a name="l00069"></a>00069             <span class="keyword">case</span>(2)
<a name="l00070"></a>00070                 <span class="keyword">select</span> <span class="keyword">case</span>(j)
<a name="l00071"></a>00071                     <span class="keyword">case</span>(1)
<a name="l00072"></a>00072                         v = (1.0d0-eta2)/4.0d0
<a name="l00073"></a>00073                     <span class="keyword">case</span>(2)
<a name="l00074"></a>00074                         v = -(eta1+1.0d0)/4.0d0
<a name="l00075"></a>00075                     <span class="keyword">case</span> default
<a name="l00076"></a>00076                         v = 0.0d0
<a name="l00077"></a>00077                 <span class="keyword">end select</span>
<a name="l00078"></a>00078             <span class="keyword">case</span>(3)
<a name="l00079"></a>00079                 <span class="keyword">select</span> <span class="keyword">case</span>(j)
<a name="l00080"></a>00080                     <span class="keyword">case</span>(1)
<a name="l00081"></a>00081                         v = (eta2+1.0d0)/4.0d0
<a name="l00082"></a>00082                     <span class="keyword">case</span>(2)
<a name="l00083"></a>00083                         v = (eta1+1.0d0)/4.0d0
<a name="l00084"></a>00084                     <span class="keyword">case</span> default
<a name="l00085"></a>00085                         v = 0.0d0
<a name="l00086"></a>00086                 <span class="keyword">end select</span>
<a name="l00087"></a>00087             <span class="keyword">case</span>(4)
<a name="l00088"></a>00088                 <span class="keyword">select</span> <span class="keyword">case</span>(j)
<a name="l00089"></a>00089                     <span class="keyword">case</span>(1)
<a name="l00090"></a>00090                         v = -(eta2+1.0d0)/4.0d0
<a name="l00091"></a>00091                     <span class="keyword">case</span>(2)
<a name="l00092"></a>00092                         v = (1.0d0-eta1)/4.0d0
<a name="l00093"></a>00093                     <span class="keyword">case</span> default
<a name="l00094"></a>00094                         v = 0.0d0
<a name="l00095"></a>00095                 <span class="keyword">end select</span>
<a name="l00096"></a>00096         <span class="keyword">end select</span>
<a name="l00097"></a>00097 <span class="keyword">    end function</span>
<a name="l00098"></a>00098 
<a name="l00099"></a><a class="code" href="class_square_element_manipulation.html#a2006374fdc93d6dff86e8266fc9bf5a3">00099</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>DeterminantInverseJacobian(X, eta1, eta2) result (v)
<a name="l00100"></a>00100         <span class="keyword">implicit none</span>
<a name="l00101"></a>00101         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(4,2)</span>, <span class="keywordtype">intent(in)</span> :: X
<a name="l00102"></a>00102         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: eta1
<a name="l00103"></a>00103         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: eta2
<a name="l00104"></a>00104 
<a name="l00105"></a>00105         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(2,2)</span> :: Jacob
<a name="l00106"></a>00106         <span class="keywordtype">real(kind=8)</span> :: v
<a name="l00107"></a>00107         <span class="keywordtype">integer(kind=1)</span> :: i, j, k
<a name="l00108"></a>00108 
<a name="l00109"></a>00109         Jacob = 0.0d0
<a name="l00110"></a>00110 
<a name="l00111"></a>00111         forall(i=1:2, j=1:2, k = 1:4)  Jacob(i,j) = Jacob(i,j) + X(k,i) * dphi(k,j, eta1, eta2)
<a name="l00112"></a>00112 
<a name="l00113"></a>00113         call Invert2(Jacob)
<a name="l00114"></a>00114 
<a name="l00115"></a>00115         v = Determinant2(Jacob)
<a name="l00116"></a>00116 <span class="keyword">    end function</span>
<a name="l00117"></a>00117 
<a name="l00118"></a><a class="code" href="class_square_element_manipulation.html#a6dd776b19d41a4b069de7ffe01cc4f09">00118</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>OuterVector() result (vector)
<a name="l00119"></a>00119         <span class="keyword">implicit none</span>
<a name="l00120"></a>00120         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(4,2)</span> :: vector
<a name="l00121"></a>00121 
<a name="l00122"></a>00122         vector = 0.0d0
<a name="l00123"></a>00123         vector(1,2) = -1.0d0
<a name="l00124"></a>00124         vector(2,1) =  1.0d0
<a name="l00125"></a>00125         vector(3,2) =  1.0d0
<a name="l00126"></a>00126         vector(4,1) = -1.0d0
<a name="l00127"></a>00127 <span class="keyword">    end function</span>
<a name="l00128"></a>00128 
<a name="l00129"></a><a class="code" href="class_square_element_manipulation.html#aef036773975448a9dd773c51056b0994">00129</a>     <span class="keyword">subroutine </span>SetMatrixSquareElement( this, integration )
<a name="l00130"></a>00130         <span class="keyword">implicit none</span>
<a name="l00131"></a>00131         <span class="keywordtype">type(SquareElement)</span>, <span class="keywordtype">intent(inout)</span> :: this
<a name="l00132"></a>00132         <span class="keywordtype">integer</span>, <span class="keywordtype">intent(in)</span> :: integration
<a name="l00133"></a>00133 
<a name="l00134"></a>00134 <span class="keyword">    end subroutine</span>
<a name="l00135"></a>00135 
<a name="l00136"></a><a class="code" href="class_square_element_manipulation.html#ad1b0d392380269eb0dd25a0afd611793">00136</a>     <span class="keyword">subroutine </span>SetMatricesE( this, X )
<a name="l00137"></a>00137         <span class="keyword">implicit none</span>
<a name="l00138"></a>00138         <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: IntPoints = 3
<a name="l00139"></a>00139         <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: nSides = 4
<a name="l00140"></a>00140         <span class="keywordtype">type(SquareElement)</span>, <span class="keywordtype">intent(inout)</span> :: this
<a name="l00141"></a>00141         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(4,2)</span>, <span class="keywordtype">intent(in)</span> :: X
<a name="l00142"></a>00142 
<a name="l00143"></a>00143         <span class="keywordtype">integer(kind=1)</span> :: i, j <span class="comment">! matrix counter</span>
<a name="l00144"></a>00144         <span class="keywordtype">integer</span> :: k, l <span class="comment">! integration points counter</span>
<a name="l00145"></a>00145 
<a name="l00146"></a>00146         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(IntPoints)</span> :: points, weights
<a name="l00147"></a>00147         <span class="keywordtype">real(kind=8)</span> :: local
<a name="l00148"></a>00148 
<a name="l00149"></a>00149         points = LinearIntegrationPoints(IntPoints)
<a name="l00150"></a>00150 
<a name="l00151"></a>00151         weights = LinearIntegrationWeights(IntPoints)
<a name="l00152"></a>00152 
<a name="l00153"></a>00153         forall(i = 1:nSides, j = 1:nSides, k = 1:IntPoints, l = 1:IntPoints)
<a name="l00154"></a>00154             local = weights(k)*weights(l) * phi( i,points(k),points(l) )*phi( j,points(k),points(l) ) * &amp;
<a name="l00155"></a>00155                             DeterminantInverseJacobian( X, points(k), points(l) )
<a name="l00156"></a>00156             <span class="comment">! First Diagonal Block</span>
<a name="l00157"></a>00157             this%Matrix(i,j) = this%Matrix(i,j) + local
<a name="l00158"></a>00158             <span class="comment">! Second Diagonal Block</span>
<a name="l00159"></a>00159             this%Matrix(i+nSides,j+nSides) = this%Matrix(i+nSides,j+nSides) + local
<a name="l00160"></a>00160         <span class="keyword">end</span> forall
<a name="l00161"></a>00161 <span class="keyword">    end subroutine</span>
<a name="l00162"></a>00162 
<a name="l00163"></a><a class="code" href="class_square_element_manipulation.html#a64f477d4bfcfd60caad97c48dd936a60">00163</a>     <span class="keyword">subroutine </span>SetMatricesExx_i( this, X, condutividadeTermica )
<a name="l00164"></a>00164         <span class="keyword">implicit none</span>
<a name="l00165"></a>00165         <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: IntPoints = 3
<a name="l00166"></a>00166         <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: nSides = 4
<a name="l00167"></a>00167         <span class="keywordtype">type(SquareElement)</span>, <span class="keywordtype">intent(inout)</span> :: this
<a name="l00168"></a>00168         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(4,2)</span>, <span class="keywordtype">intent(in)</span> :: X
<a name="l00169"></a>00169         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">intent(in)</span> :: condutividadeTermica
<a name="l00170"></a>00170 
<a name="l00171"></a>00171         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(4,2)</span> :: n
<a name="l00172"></a>00172 
<a name="l00173"></a>00173         <span class="keywordtype">real(kind=8)</span> :: local
<a name="l00174"></a>00174         <span class="keywordtype">integer</span> :: i, j
<a name="l00175"></a>00175         <span class="keywordtype">integer</span> :: k, l
<a name="l00176"></a>00176 
<a name="l00177"></a>00177         n = OuterVector()
<a name="l00178"></a>00178 
<a name="l00179"></a>00179         forall(i = 1:nSides)
<a name="l00180"></a>00180 
<a name="l00181"></a>00181 
<a name="l00182"></a>00182         <span class="keyword">end</span> forall
<a name="l00183"></a>00183 
<a name="l00184"></a>00184 <span class="keyword">    end subroutine</span>
<a name="l00185"></a>00185 <span class="keyword">end module</span>
<a name="l00186"></a>00186 
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